Compressive Sensing Methods Using Structure Information And Its Application In CT Image Reconstruction

Compressive sensing is a new theory in recent years,and it has a wide range of applications in many fields,such as medical image processing,wireless sensor networks,radar,remote sensing Image processing,spectral analysis,biological sensing and so on.The reconstruction of signal is an important part of compressive sensing theory,and it is also the key point of whether compressive sensing can be applied in practice.This thesis mainly studies how to reconstruct one-dimensional jointly sparse signal and two-dimensional CT image by using the methods of compressive sensing based on structure information respectively.In this paper,based on the prior information of joint sparsity between signals,a novel algorithm is proposed to address sparse signal recovery problem of the MMV model.Specifically,it is assumed that the non-0 elements of the vector obey the Gaussian distribution,and then the expected model is deduced by using the Bayesian method and the maximum a posteriori estimation.By means of block coordinate descent method,the objective functions of all sparse vectors to be solved are established.A mixture of weightedl₁norm penalty and al₂norm squared penalty are developed,which corresponds to the optimization of 0elements and non-0 elements in signals respectively.Then the algorithm proposed in this thesis uses a re-weighted method to solve these minimization problems sequently and iteratively.In each iteration,every vector is calculated based on all the obtained solutions which could provide the prior information on the sparsity structure and help modify the values of weights.Through experiments on simulation data and clinical data,the algorithm has been proved to be robust and anti-noise,and in most cases it behaves better than other algorithms.For the reconstruction of two-dimensional CT images,a mixed one-bit compressive sensing model using measurements’one-bit information is proposed for the overexposure problem in CT reconstruction in this thesis,and two solutions for this model are proposed.The first method uses the ADMM method to solve the variables in the model in turn,and uses the FISTA algorithm to solve the two-dimensional image variables iteratively.In the experiments of overexposed knee model and clinical brain data,the algorithm shows its strong ability of inhibiting artifacts.The second method is based on Chambolle and Pock algorithm.It transforms the minimization solution of the original convex problem in mixed one-bit compressive sensing model into the solution of the saddle point of its original duality problem.The Shepp-logan projection data with overexposure and few sampling are reconstructed,which proves that the proposed algorithm has higher reconstruction accuracy and better ability to suppress artifacts than some classical algorithms,and the image quality in details is better than that of the previous algorithm which is based on ADMM.In addition,the re-weighted multi-scale total variation regularization is introduced in the model,and the former algorithm is improved based on Chambolle-Pock algorithm.The experiment proves that the improved algorithm can suppress streak artifacts in limited angle problems more effectively than the former algorithm.